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[prcantos]

Hi. Recently I received this spessartine + feldspar (microcline) + quartz specimen from Fujian (China).

The garnet crystals are really sharp, and the microscope reveals many interesting faces.

I can recognize the trapezohedron {112}, which is the dominant form, and the rhombdodecahedron {110} (of course I am using minimal Miller indices as I haven't measured the real dihedral angles).

There are apparently other thin faces in the edges of the trapeziums. The thin faces that meet at the 2-fold vertices may be {120} faces (tetrakis-hexahedron), and the ones meeting at the 3-fold vertices might be {233} (triakis-octahedron).

My questions are:

1) Are these thin faces real faces of this crystal, or are they a kind of striation, optical effects, dissolution zones in the crystal...?

2) In case they are true faces, have I identified the forms correctly? I mean: tetrakis-hexahedron faces meeting at the 2-fold vertices and triakis-octahedron faces meeting at the 3-fold vertices.

What do you think? Thank you very much.

[Bob Carnein]

It looks to me like there are actually 2 faces on each of the"edges" you refer to. If that's the case, then 6 faces meet at the end of each 3-fold axis. Because there are 8 "ends" of 3-fold axes, that would total 48 faces, making the form a hexoctahedron.

[marco campos-venuti]

The 110 faces look to be responsible for the striation.

[prcantos]

[Pete Richards]

Let me interject a bit of Miller index algebra into this discussion. This can be documented by reference to many standard texts, and it makes solving such problems much easier!

Rule 1: If you want to find the face that bevels two other faces (i.e. forms a single face that has parallel edges in intersection with them), add the Miller indices, index by index. So for the faces (211) and (21-1), the beveling face is (420)=(210), and this is true for every such edge on the specimen, so the beveling form is {210}. For the faces (211) and (121) - Pablos's second case, the beveling face is (332) as he inferred, and the general form for that bevel is {332}.

Rule 2: Now, if we want not one face modifying an edge but two parallel faces, we can use a more general relationship, that n(hkl1)+m(hkl2) is a form that works for any value of n and m. For example, this could be 3*(211)+2*(121)=6 3 3 + 2 4 2= 8 7 5 = (875). Or one could add one face to the bevel: (211)+(210) = (421) - with any weighting between them via n and m values. Any faces so generated will satisfy the criterion that they are two-fold around the edge in question, and are strictly parallel to this edge. (I should be careful and state that the two-fold statement only applies in certain higher symmetry classes such as garnet, but the strict parallelism applies in all cases).

The question of which form is the right choice then becomes one of what the angles are between the main faces and the beveling faces. Without measurements, this question cannot be answered unambiguously. However, one of the empirical laws of crystallography is that Miller indices of crystal faces tend to be small integers, so Pablo' 100 135 165 is approximately 1.0 1.33 1.67 or (345) when cleared of fractions. (345) is equal to 2*(211)+(121)=4 2 2 + 1 2 1=5 4 3 =(by symmetry) (345), or the form {345}.

It is also interesting to note that no single hexoctahedron can provide double bevels both to the edges that lead to the cube axes and to those that lead to the three-fold axes, coded blue and white in Pablo' first drawing respectively. I cannot prove this algebraically, but geometrically it appears to be quite evident: If you stick in a form that will bevel one of the edges leading to the three-fold axis, it will not bevel the very differently oriented edge leading to the four-fold axis, and vise versa.

If (as I cannot tell) all of these edges have double bevels of roughly equal size and angle, this strongly suggests that these modifying faces are due to dissolution rather than crystal growth, in which case they are not true crystal faces. The irregularity shown in some images tends to reinforce this suggestion.

I think Marco's images show true growth faces with alternation between dodecahedron and trapezohedron, but they are a different issue from Pablo' crystals.


Whew! I almost blew this response away after a half hour of working on it!! Now, fifteen minutes later, I hope you can get some good stuff from it! Meanwhile, for those who are tuned into American basketball, I'm about to go and hope that the Cleveland Cavaliers can win again!

[marco campos-venuti]

Your Cleveland Cavaliers won Pete, so probably you are now busy drinking beer and honking your horn in the streets!
When you'll be back I just have a question for you: the faces due to dissolution are not true crystal faces, but they are true crystal lattice faces. So what is the difference? They also have indexes. Or not?

[prcantos]

[Pete Richards]

[prcantos]